Associated manuscript: Developing prediction models to estimate the joint risk of both-of-two survival outcomes: a comparison of techniques

Section 1. Simulation: Calibration curves of product method

These are the same plot type as Figure 2 in the manuscript, plotted for every sample size

Figure S1.1: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S1.2: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S1.3: Calibration curves of the product method across the 1000 simulation iterations, panelled by simulation scenario (n = 5000)

Section 2. Simulation: Median calibration curve across the 1000 simulation iterations (average calibration) for each data generating mechanism, scenario and sample size

Figure S2.1: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.2: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.3: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.4: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.5: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.6: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario LH, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.7: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.8: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.9: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.10: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.11: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S2.12: Median calibration curve across the 1000 simulation iterations (average calibration) for scenario HH, (n = 5000)

Section 3. Simulation: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for each data generating mechanism, scenario and sample size

Figure S3.1: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.2: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.3: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.4: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.5: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.6: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario LH, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.7: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.8: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.9: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HL, (n = 5000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.10: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 1000)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.11: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 2500)---------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Figure S3.12: 5 - 95 percentile range in calibration curves across the 1000 simulation iterations (calibration variation) for scenario HH, (n = 5000)

Section 4. Simulation: Discrimination tables

Table S4.1: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.79 (0.061) 0.785 (0.063) 0.782 (0.065) 0.79 (0.061) 0.79 (0.062) 0.79 (0.061) 0.79 (0.061) 0.79 (0.061)
DGM2 (c-clay) 0.788 (0.06) 0.781 (0.064) 0.778 (0.067) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06) 0.788 (0.06)
DGM3 (c-gumb) 0.757 (0.065) 0.749 (0.068) 0.746 (0.071) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065) 0.757 (0.065)
DGM4 (c-frank) 0.779 (0.061) 0.773 (0.064) 0.771 (0.065) 0.779 (0.061) 0.779 (0.061) 0.779 (0.062) 0.779 (0.061) 0.779 (0.061)
DGM5 (f-norm) 0.779 (0.063) 0.773 (0.065) 0.77 (0.067) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063) 0.779 (0.063)
DGM6 (f-gam) 0.78 (0.06) 0.774 (0.064) 0.771 (0.064) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06) 0.78 (0.06)

Table S4.2: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.791 (0.064) 0.788 (0.065) 0.788 (0.065) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064) 0.791 (0.064)
DGM2 (c-clay) 0.786 (0.062) 0.784 (0.062) 0.783 (0.063) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062) 0.786 (0.062)
DGM3 (c-gumb) 0.758 (0.064) 0.756 (0.065) 0.756 (0.065) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064) 0.758 (0.064)
DGM4 (c-frank) 0.78 (0.062) 0.777 (0.063) 0.777 (0.063) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062) 0.78 (0.062)
DGM5 (f-norm) 0.778 (0.061) 0.776 (0.061) 0.776 (0.061) 0.778 (0.061) 0.777 (0.061) 0.778 (0.061) 0.777 (0.061) 0.777 (0.061)
DGM6 (f-gam) 0.787 (0.06) 0.784 (0.06) 0.784 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06) 0.787 (0.06)

Table S4.3: Harrel's C-statistic (mean (sd)) for scenario LL, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.791 (0.06) 0.79 (0.06) 0.79 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06) 0.791 (0.06)
DGM2 (c-clay) 0.783 (0.061) 0.782 (0.062) 0.782 (0.062) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061) 0.783 (0.061)
DGM3 (c-gumb) 0.759 (0.062) 0.758 (0.063) 0.757 (0.063) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062) 0.759 (0.062)
DGM4 (c-frank) 0.777 (0.063) 0.777 (0.062) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063) 0.777 (0.063)
DGM5 (f-norm) 0.78 (0.061) 0.779 (0.061) 0.779 (0.062) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061) 0.78 (0.061)
DGM6 (f-gam) 0.781 (0.061) 0.78 (0.061) 0.78 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061) 0.781 (0.061)

Table S4.4: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.785 (0.054) 0.781 (0.056) 0.779 (0.057) 0.785 (0.054) 0.784 (0.055) 0.785 (0.054) 0.784 (0.054) 0.784 (0.054)
DGM2 (c-clay) 0.783 (0.054) 0.778 (0.056) 0.775 (0.057) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054) 0.783 (0.054)
DGM3 (c-gumb) 0.733 (0.063) 0.726 (0.066) 0.723 (0.067) 0.733 (0.063) 0.733 (0.063) 0.733 (0.063) 0.732 (0.063) 0.732 (0.063)
DGM4 (c-frank) 0.772 (0.056) 0.767 (0.058) 0.766 (0.059) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056) 0.772 (0.056)
DGM5 (f-norm) 0.763 (0.057) 0.757 (0.059) 0.756 (0.059) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057)
DGM6 (f-gam) 0.766 (0.056) 0.761 (0.06) 0.76 (0.06) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056) 0.766 (0.056)

Table S4.5: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.785 (0.055) 0.783 (0.055) 0.783 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055) 0.785 (0.055)
DGM2 (c-clay) 0.781 (0.056) 0.779 (0.056) 0.779 (0.057) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056) 0.781 (0.056)
DGM3 (c-gumb) 0.737 (0.061) 0.735 (0.062) 0.735 (0.062) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061) 0.737 (0.061)
DGM4 (c-frank) 0.773 (0.057) 0.771 (0.057) 0.771 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057) 0.773 (0.057)
DGM5 (f-norm) 0.763 (0.057) 0.761 (0.057) 0.761 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057) 0.763 (0.057)
DGM6 (f-gam) 0.77 (0.056) 0.768 (0.056) 0.768 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056) 0.77 (0.056)

Table S4.6: Harrel's C-statistic (mean (sd)) for scenario LH, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.788 (0.054) 0.787 (0.054) 0.787 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054) 0.788 (0.054)
DGM2 (c-clay) 0.777 (0.056) 0.776 (0.056) 0.776 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056) 0.777 (0.056)
DGM3 (c-gumb) 0.735 (0.059) 0.734 (0.059) 0.734 (0.06) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059) 0.735 (0.059)
DGM4 (c-frank) 0.77 (0.055) 0.77 (0.054) 0.77 (0.054) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055) 0.77 (0.055)
DGM5 (f-norm) 0.764 (0.056) 0.763 (0.056) 0.763 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056) 0.764 (0.056)
DGM6 (f-gam) 0.769 (0.058) 0.767 (0.058) 0.767 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058) 0.768 (0.058)

Table S4.7: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.019) 0.794 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019)
DGM3 (c-gumb) 0.766 (0.021) 0.765 (0.021) 0.765 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021)
DGM4 (c-frank) 0.786 (0.018) 0.785 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018) 0.786 (0.018)
DGM5 (f-norm) 0.779 (0.02) 0.778 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02) 0.779 (0.02)
DGM6 (f-gam) 0.788 (0.019) 0.787 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02) 0.788 (0.02)

Table S4.8: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019) 0.795 (0.019)
DGM3 (c-gumb) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.766 (0.021) 0.767 (0.021) 0.767 (0.021) 0.767 (0.021) 0.767 (0.021)
DGM4 (c-frank) 0.786 (0.019) 0.785 (0.02) 0.786 (0.02) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019) 0.786 (0.019)
DGM5 (f-norm) 0.78 (0.019) 0.779 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019) 0.78 (0.019)
DGM6 (f-gam) 0.789 (0.019) 0.788 (0.019) 0.788 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019) 0.789 (0.019)

Table S4.9: Harrel's C-statistic (mean (sd)) for scenario HL, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.794 (0.019) 0.793 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019) 0.794 (0.019)
DGM2 (c-clay) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018) 0.795 (0.018)
DGM3 (c-gumb) 0.766 (0.02) 0.765 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02) 0.766 (0.02)
DGM4 (c-frank) 0.785 (0.02) 0.784 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02) 0.785 (0.02)
DGM5 (f-norm) 0.779 (0.019) 0.778 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019) 0.779 (0.019)
DGM6 (f-gam) 0.79 (0.018) 0.789 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018) 0.79 (0.018)

Table S4.10: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 1000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.776 (0.018) 0.776 (0.018) 0.776 (0.017) 0.776 (0.017) 0.776 (0.018) 0.776 (0.017) 0.776 (0.017) 0.776 (0.017)
DGM2 (c-clay) 0.774 (0.018) 0.773 (0.018) 0.774 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018) 0.775 (0.018)
DGM3 (c-gumb) 0.731 (0.02) 0.73 (0.02) 0.73 (0.02) 0.731 (0.02) 0.732 (0.02) 0.732 (0.02) 0.732 (0.02) 0.732 (0.02)
DGM4 (c-frank) 0.761 (0.017) 0.759 (0.017) 0.761 (0.017) 0.761 (0.021) 0.761 (0.017) 0.761 (0.017) 0.761 (0.017) 0.761 (0.017)
DGM5 (f-norm) 0.747 (0.019) 0.746 (0.019) 0.746 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019) 0.747 (0.019)
DGM6 (f-gam) 0.77 (0.018) 0.769 (0.018) 0.77 (0.018) 0.77 (0.018) 0.77 (0.017) 0.77 (0.018) 0.771 (0.018) 0.771 (0.018)

Table S4.11: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 2500)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018)
DGM2 (c-clay) 0.774 (0.018) 0.773 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018) 0.774 (0.018)
DGM3 (c-gumb) 0.732 (0.02) 0.731 (0.02) 0.732 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02)
DGM4 (c-frank) 0.76 (0.019) 0.759 (0.019) 0.76 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019) 0.761 (0.019)
DGM5 (f-norm) 0.747 (0.018) 0.746 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.018) 0.747 (0.019) 0.747 (0.019)
DGM6 (f-gam) 0.771 (0.017) 0.77 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017) 0.771 (0.017)

Table S4.12: Harrel's C-statistic (mean (sd)) for scenario HH, (n = 5000)

product joint-o msm c-clay c-gumb c-frank f-norm f-gam
DGM1 (msm) 0.778 (0.018) 0.777 (0.018) 0.778 (0.018) 0.778 (0.018) 0.778 (0.018) 0.777 (0.018) 0.777 (0.018) 0.777 (0.018)
DGM2 (c-clay) 0.773 (0.017) 0.772 (0.018) 0.773 (0.017) 0.774 (0.017) 0.773 (0.017) 0.774 (0.017) 0.774 (0.017) 0.774 (0.017)
DGM3 (c-gumb) 0.732 (0.02) 0.731 (0.02) 0.731 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02) 0.733 (0.02)
DGM4 (c-frank) 0.759 (0.018) 0.758 (0.018) 0.759 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018) 0.76 (0.018)
DGM5 (f-norm) 0.746 (0.017) 0.745 (0.017) 0.745 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017) 0.746 (0.017)
DGM6 (f-gam) 0.771 (0.018) 0.771 (0.018) 0.771 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018) 0.772 (0.018)

Table S4.13: Harrel's C-statistic (mean (sd)) for scenario LN

n = 1000 n = 2500 n = 5000
DGM1 (msm) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM2 (c-clay) 0.783 (0.074) 0.788 (0.069) 0.786 (0.066)
DGM3 (c-gumb) 0.779 (0.077) 0.788 (0.069) 0.786 (0.066)
DGM4 (c-frank) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM5 (f-norm) 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
DGM6 (f-gam) 0.792 (0.067) 0.79 (0.069) 0.787 (0.066)
NA 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)
NA 0.792 (0.067) 0.79 (0.069) 0.788 (0.066)

Table S4.14: Harrel's C-statistic (mean (sd)) for scenario HN

n = 1000 n = 2500 n = 5000
DGM1 (msm) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM2 (c-clay) 0.809 (0.02) 0.809 (0.021) 0.809 (0.019)
DGM3 (c-gumb) 0.809 (0.02) 0.809 (0.021) 0.809 (0.019)
DGM4 (c-frank) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM5 (f-norm) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
DGM6 (f-gam) 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
NA 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)
NA 0.809 (0.02) 0.809 (0.02) 0.809 (0.019)

Section 5. Simulation: event rates

Table S5.1: Mean (sd) of the number of uncensored events for outcome A across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 94 (9) 94 (9) 94 (9) 94 (9) 94 (9) 94 (9)
LL 94 (9) 94 (9) 94 (9) 94 (9) 95 (9) 94 (10)
LH 93 (10) 94 (9) 94 (9) 94 (9) 96 (9) 96 (9)
HN 285 (14) 285 (14) 285 (14) 285 (14) 285 (14) 285 (14)
HL 281 (14) 285 (14) 285 (14) 285 (14) 286 (15) 287 (14)
HH 280 (15) 285 (14) 285 (15) 285 (14) 291 (14) 288 (15)

Table S5.2: Mean (sd) of the number of uncensored events for outcome B across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 95 (9) 95 (9) 95 (9) 95 (9) 95 (9) 95 (9)
LL 95 (9) 95 (9) 95 (10) 95 (9) 97 (9) 95 (9)
LH 94 (9) 95 (9) 95 (10) 95 (9) 97 (9) 96 (9)
HN 288 (14) 288 (14) 288 (14) 288 (14) 288 (14) 288 (14)
HL 289 (15) 288 (14) 287 (15) 288 (14) 289 (14) 289 (14)
HH 286 (14) 288 (14) 288 (15) 287 (14) 292 (14) 292 (14)

Table S5.3: Mean (sd) of the number of uncensored events for outcome AB across 1000 simulation iterations, n = 1000

DGM1 (msm) DGM2 (c-clay) DGM3 (c-gumb) DGM4 (c-frank) DGM5 (f-norm) DGM6 (f-gam)
LN 12 (3) 12 (3) 12 (3) 12 (3) 12 (3) 12 (3)
LL 14 (4) 14 (4) 14 (4) 14 (4) 14 (4) 14 (4)
LH 17 (4) 17 (4) 17 (4) 17 (4) 18 (4) 18 (4)
HN 105 (10) 105 (10) 105 (10) 105 (10) 105 (10) 105 (10)
HL 126 (10) 126 (10) 127 (11) 126 (10) 129 (11) 127 (10)
HH 156 (11) 158 (11) 160 (12) 158 (11) 159 (12) 157 (12)

Section 6: Clinical example supplementary figures and tables

Table S6.1: Baseline data for development and validation cohorts

  development validation Overall
(N=100000) (N=100000) (N=200000)
Age
  Mean (SD) 68.9 (± 5.51) 68.9 (± 5.48) 68.9 (± 5.50)
gender
  0 44176 (44.2%) 44428 (44.4%) 88604 (44.3%)
  1 55824 (55.8%) 55572 (55.6%) 111396 (55.7%)
BMI
  Mean (SD) 26.9 (± 4.99) 26.9 (± 4.98) 26.9 (± 4.99)
Cholesterol/HDL ratio
  Mean (SD) 3.82 (± 1.17) 3.83 (± 1.17) 3.82 (± 1.17)
Ethnicity
  White 94682 (94.7%) 94680 (94.7%) 189362 (94.7%)
  Mixed race 405 (0.405%) 370 (0.370%) 775 (0.388%)
  South asian 2379 (2.38%) 2456 (2.46%) 4835 (2.42%)
  Black 1806 (1.81%) 1776 (1.78%) 3582 (1.79%)
  Chinese and other 728 (0.728%) 718 (0.718%) 1446 (0.723%)
  Other 0 (0%) 0 (0%) 0 (0%)
SBP
  Mean (SD) 139 (± 17.6) 139 (± 17.6) 139 (± 17.6)
Smoking status
  Never 37958 (38.0%) 37898 (37.9%) 75856 (37.9%)
  Ex 34372 (34.4%) 34086 (34.1%) 68458 (34.2%)
  Current 27670 (27.7%) 28016 (28.0%) 55686 (27.8%)
IMD
  1 (most deprived) 26032 (26.0%) 25911 (25.9%) 51943 (26.0%)
  2 22832 (22.8%) 22984 (23.0%) 45816 (22.9%)
  3 20150 (20.2%) 20271 (20.3%) 40421 (20.2%)
  4 17087 (17.1%) 16878 (16.9%) 33965 (17.0%)
  5 (least deprived) 13899 (13.9%) 13956 (14.0%) 27855 (13.9%)

Table S6.2: Outcome data for development and validation cohorts

Metric Development Validation
T2D Number at risk 1e+05 1e+05
T2D Time at risk (days) 285073504 283633278
T2D Number of events 8018 8039
T2D Rate (per 1000 person years) 10.27 10.35
CVD Number at risk 1e+05 1e+05
CVD Time at risk (days) 269795825 268104593
CVD Number of events 17638 17605
CVD Rate (per 1000 person years) 23.88 23.98

Figure S6.1: Graphical calibration curves for each method in the clinical example over the entire range of predicted risk

Figure S6.2: Observed vs predicted risk by decile of predicted risk for each method in the clinical example